Is it disrespectful to choose not to divulge your own pronouns?

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No. It's absolutely trivially easy to simply do so, but it's also completely unnecessary unless someone wants to disclose it for their own purposes or just to support those who do. As long as people have the option to disclose it without being shamed, that's where it should stop. The idea that one needs to do so to show support is just good intentions taken too far.